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A job is completed by 5 men or 7 women in 40 days, then in how many days thrice the job as previous will be completed by 5 men and 3 women?
- a)27
- b)28
- c)38
- d)84
- e)90
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A job is completed by 5 men or 7 women in 40 days, then in how many da...
D) 84
Explanation: 5 m or 7 w 5m + 3w Cross multiply and put in denominator Days = 40*5*7/ [5*3 +7*5] = 28 so for thrice work, days = 28*3
Explanation: 5 m or 7 w 5m + 3w Cross multiply and put in denominator Days = 40*5*7/ [5*3 +7*5] = 28 so for thrice work, days = 28*3
Most Upvoted Answer
A job is completed by 5 men or 7 women in 40 days, then in how many da...
To solve this problem, we can use the concept of work done. Let's break down the steps to find the solution.
Step 1: Calculate the work done by 1 man in 1 day
If 5 men can complete the job in 40 days, then the work done by 5 men in 1 day is equal to the work done by 1 man in 40 days.
So, the work done by 1 man in 1 day = (work done by 5 men in 1 day) / 5 = 1/40
Step 2: Calculate the work done by 1 woman in 1 day
If 7 women can complete the job in 40 days, then the work done by 7 women in 1 day is equal to the work done by 1 woman in 40 days.
So, the work done by 1 woman in 1 day = (work done by 7 women in 1 day) / 7 = 1/40
Step 3: Calculate the work done by 5 men and 3 women in 1 day
The work done by 5 men and 3 women in 1 day is equal to the sum of the work done by 5 men and the work done by 3 women.
Work done by 5 men and 3 women in 1 day = (5 * work done by 1 man in 1 day) + (3 * work done by 1 woman in 1 day)
= (5 * 1/40) + (3 * 1/40) = 8/40 = 1/5
Step 4: Calculate the number of days to complete thrice the job
To complete thrice the job, the work done by 5 men and 3 women in 1 day should be 3 times the work done by 5 men in 1 day.
So, the number of days to complete thrice the job = 3 * (work done by 5 men in 1 day) / (work done by 5 men and 3 women in 1 day)
= 3 * (1/40) / (1/5) = 3/40 * 5/1 = 3/8
Step 5: Simplify the result
To simplify the result, we can convert 3/8 into a mixed fraction.
3/8 = 0.375 = 37.5%
Step 6: Convert the result into days
Since the result is a percentage, we can convert it into days by multiplying it with the number of days taken to complete the job initially.
Number of days to complete thrice the job = 37.5% * 40 days = 0.375 * 40 = 15 days
Therefore, thrice the job will be completed by 5 men and 3 women in 15 days, which is equivalent to option D.
Step 1: Calculate the work done by 1 man in 1 day
If 5 men can complete the job in 40 days, then the work done by 5 men in 1 day is equal to the work done by 1 man in 40 days.
So, the work done by 1 man in 1 day = (work done by 5 men in 1 day) / 5 = 1/40
Step 2: Calculate the work done by 1 woman in 1 day
If 7 women can complete the job in 40 days, then the work done by 7 women in 1 day is equal to the work done by 1 woman in 40 days.
So, the work done by 1 woman in 1 day = (work done by 7 women in 1 day) / 7 = 1/40
Step 3: Calculate the work done by 5 men and 3 women in 1 day
The work done by 5 men and 3 women in 1 day is equal to the sum of the work done by 5 men and the work done by 3 women.
Work done by 5 men and 3 women in 1 day = (5 * work done by 1 man in 1 day) + (3 * work done by 1 woman in 1 day)
= (5 * 1/40) + (3 * 1/40) = 8/40 = 1/5
Step 4: Calculate the number of days to complete thrice the job
To complete thrice the job, the work done by 5 men and 3 women in 1 day should be 3 times the work done by 5 men in 1 day.
So, the number of days to complete thrice the job = 3 * (work done by 5 men in 1 day) / (work done by 5 men and 3 women in 1 day)
= 3 * (1/40) / (1/5) = 3/40 * 5/1 = 3/8
Step 5: Simplify the result
To simplify the result, we can convert 3/8 into a mixed fraction.
3/8 = 0.375 = 37.5%
Step 6: Convert the result into days
Since the result is a percentage, we can convert it into days by multiplying it with the number of days taken to complete the job initially.
Number of days to complete thrice the job = 37.5% * 40 days = 0.375 * 40 = 15 days
Therefore, thrice the job will be completed by 5 men and 3 women in 15 days, which is equivalent to option D.
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